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title: "A high-speed train travels at a constant velocity of \\(50\\text{ m/s}\\) along a straight, horizontal track. At this speed, its engines deliver \\(2.0\\text{ MW}\\) of mechanical power to overcome an aerodynamic drag force modeled by \\(F_D = b v^2\\), where \\(b\\) is a positive constant and \\(v\\) is the speed of the train. Assuming all other resistive forces are negligible, what mechanical power must the engines deliver for the train to maintain a constant velocity of \\(100\\text{ m/s}\\)?"
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url: "https://nerd-notes.com/ubq/123971/"
date_modified: "2026-09-28T13:29:46+00:00"
---

# A high-speed train travels at a constant velocity of \(50\text{ m/s}\) along a straight, horizontal track. At this speed, its engines deliver \(2.0\text{ MW}\) of mechanical power to overcome an aerodynamic drag force modeled by \(F_D = b v^2\), where \(b\) is a positive constant and \(v\) is the speed of the train. Assuming all other resistive forces are negligible, what mechanical power must the engines deliver for the train to maintain a constant velocity of \(100\text{ m/s}\)?

A high-speed train travels at a constant velocity of \(50\text{ m/s}\) along a straight, horizontal track. At this speed, its engines deliver \(2.0\text{ MW}\) of mechanical power to overcome an aerodynamic drag force modeled by \(F_D = b v^2\), where \(b\) is a positive constant and \(v\) is the speed of the train. Assuming all other resistive forces are negligible, what mechanical power must the engines deliver for the train to maintain a constant velocity of \(100\text{ m/s}\)?

- **A.** \(4.0\text{ MW}\)
- **B.** \(8.0\text{ MW}\)
- **C.** \(16\text{ MW}\)
- **D.** \(32\text{ MW}\)

*The answer key and step-by-step explanation are available to logged-in users at https://nerd-notes.com/ubq/123971/*